On this page we collect the background theory, and calculations that inform the design of FINCH EYE. We organize them into chapters as following:
The starting point in the design of any optical system, after the specification of its requirements, is a basic analysis in geometric optics. Rough sizing and definition of optical components, such as focal lengths, separations, etc. may be quickly derived. Once a “first-order” design has been made, it is then refined and optimized for cost / performance (e.g., reducing aberrations across a wide field of view, reducing complexity or number of lens elements in a system, …). With FINCH EYE, we must also consider effects of physical optics, namely diffraction at the GRISM.
There are additional calculations that typically go into the design of optical systems (such as tolerance analysis, mecha-thermal-optical performance, MTF analysis, stray light analysis…) but many of them are only tractable if performed with computer software. This limits the extent of what “design calculations” can be done “on paper” before transitioning to computer-aided design with Zemax .
This section contains “flash cards” for important formulas and can serve as a reference. Most of them (if not all) can be derived from first principles and logic. Please note that citations are missing from some formulas, and the information may possibly contain uncorrected errors.
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The FINCH EYE consists of an objective lens that collects light from the ground target, a slit which “selects” a single line on the ground, a lens relay which passes the light through the GRISM, and the camera detector. The image of the ground target produced by the objective lens on the slit is re-imaged onto the camera sensor by the lens relay. However, the GRISM inside the relay disperses white light into a spectrum, so the image on the camera array will be “spatial” along one axis and “spectral” along the other. Conceptually, this is a neat idea and seems to be reasonable. But what focal length and diameter of lenses should we use? How exactly does each component have to be positioned relative to each other so that the system works?
In this lecture, we determine the basic specifications and positioning of each optical component within the system, using primarily geometrical optics considerations.
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